// Appendix D.1 (p121) of Klein and Godunov Introductory Computational Physics
// program to calculate the mass on a spring problem.
//m=k=1; therefore a=-x
//with the simple Euler method
//ak 9/7/00
//all in double precision
//small adjustments isv Jan. 2017
#include <iostream>
#include <fstream>
#include <math.h>
#include <iomanip>
#include <stdio.h>
using namespace std;


int main (int argc, char **argv)
{
   int n; // number of steps
   double v; //the velocity
   double vinit= 5.;// initial velocity
   double x;// the x-value
   double xinit= 0.;// initial position
   double energy; // the energy from mv**2/2+kx**2/2
   double step; //the step size for the euler method
   double t=0.;; //the time

    if (argc != 3) {
        fprintf(stderr, "Usage: %s <nsteps> <delta t>\n", argv[0]);
        exit(EXIT_FAILURE);
    }

    n = atoi(argv[1]);
    step= atof(argv[2]);


   int i = 0;//the loop counter
// initial conditions
   t=0;
   v=vinit;
   x=xinit;
   energy=0.5*xinit*xinit + 0.5*vinit*vinit;
   cout << t << " " << x << " " << v << " " << energy << endl;

   while(i < n)  //make n steps
      {
      v=v-step*x; //calculate the forward velocity
      x=x+step*v; //calculate the forward position
      energy=pow(x,2)/2.+pow(v,2)/2.; //energy conservation
      t=t+step;
      i=i+1;
      cout << t << " " << x << " " << v << " " << energy << endl;
      }
}